Answer:
C. 12m
Explanation:
Let the length of the shorter arm = x
Since the length of the longer arm is equal to twice the length of the shorter arm;
• The length of the longer arm = 2x
• The area of triangle ABD = 18√3 m².
Given a triangle with two sides and the included angle, the area of the triangle is calculated using the formula below:
![\begin{gathered} \text{Area}=\frac{1}{2}ab\sin \theta \\ \implies\text{Area of triangle ABD =}\frac{1}{2}bd\sin A \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7BArea%7D%3D%5Cfrac%7B1%7D%7B2%7Dab%5Csin%20%5Ctheta%20%5C%5C%20%5Cimplies%5Ctext%7BArea%20of%20triangle%20ABD%20%3D%7D%5Cfrac%7B1%7D%7B2%7Dbd%5Csin%20A%20%5Cend%7Bgathered%7D)
Therefore:
![18\sqrt[]{3}=\frac{1}{2}(x)(2x)\sin (60\degree)](https://tex.z-dn.net/?f=18%5Csqrt%5B%5D%7B3%7D%3D%5Cfrac%7B1%7D%7B2%7D%28x%29%282x%29%5Csin%20%2860%5Cdegree%29)
We solve for x.
![\begin{gathered} 18\sqrt[]{3}=\frac{2x^2}{2}\times\sin 60\degree \\ 18\sqrt[]{3}=x^2\times\frac{\sqrt[]{3}}{2} \\ \text{Multiply both sides by }\frac{2}{\sqrt[]{3}} \\ 18\sqrt[]{3}\times\frac{2}{\sqrt[]{3}}=x^2\times\frac{\sqrt[]{3}}{2}\times\frac{2}{\sqrt[]{3}} \\ x^2=36 \\ x^2=6^2 \\ x=6 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%2018%5Csqrt%5B%5D%7B3%7D%3D%5Cfrac%7B2x%5E2%7D%7B2%7D%5Ctimes%5Csin%2060%5Cdegree%20%5C%5C%2018%5Csqrt%5B%5D%7B3%7D%3Dx%5E2%5Ctimes%5Cfrac%7B%5Csqrt%5B%5D%7B3%7D%7D%7B2%7D%20%5C%5C%20%5Ctext%7BMultiply%20both%20sides%20by%20%7D%5Cfrac%7B2%7D%7B%5Csqrt%5B%5D%7B3%7D%7D%20%5C%5C%2018%5Csqrt%5B%5D%7B3%7D%5Ctimes%5Cfrac%7B2%7D%7B%5Csqrt%5B%5D%7B3%7D%7D%3Dx%5E2%5Ctimes%5Cfrac%7B%5Csqrt%5B%5D%7B3%7D%7D%7B2%7D%5Ctimes%5Cfrac%7B2%7D%7B%5Csqrt%5B%5D%7B3%7D%7D%20%5C%5C%20x%5E2%3D36%20%5C%5C%20x%5E2%3D6%5E2%20%5C%5C%20x%3D6%20%5Cend%7Bgathered%7D)
Multiply x by 2 to get the length of the longer arm:
![2x=2\times6=12m](https://tex.z-dn.net/?f=2x%3D2%5Ctimes6%3D12m)
The length of the longer arm is 12m.
C is the correct option.
Answer:
The volume of the cylinder is 120.10 square feet.
Step-by-step explanation:
Given that the radius of a cylindrical construction pipe is 1.5 ft, to determine its volume if the pipe is 17 ft long, the following calculation must be performed, knowing that the volume of a cylinder arises from multiplying the number pi by the radius at square of the cylinder, and that result by the height of the same:
3.14 x 1.5 ^ 2 x 17 = X
3.14 x 2.25 x 17 = X
7.065 x 17 = X
120.105 = X
Thus, the volume of the cylinder is 120.10 square feet.
Answer hola senior me no espanol
Step-by-step explanation:
1+1=2?????? easy IT SO EASY!!!!!!!
Factor the numerator using difference of cubes:
![a^3 - b^3 = (a-b)(a^2 +ab+b^2)](https://tex.z-dn.net/?f=a%5E3%20-%20b%5E3%20%3D%20%28a-b%29%28a%5E2%20%2Bab%2Bb%5E2%29)
a = x
b = 2
![\frac{x^3 - 8}{x-2} = \frac{(x-2)(x^2 +2x+4)}{x-2} = x^2 +2x+4](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E3%20-%208%7D%7Bx-2%7D%20%3D%20%5Cfrac%7B%28x-2%29%28x%5E2%20%2B2x%2B4%29%7D%7Bx-2%7D%20%3D%20x%5E2%20%2B2x%2B4)
Now you can evaluate limit as x=2.